Reliability calculations for a system with heterogeneous subsystem redundancy
The purpose of the paper was to study the problem of confidence estimation of basic reliability indicators, such as the system failure-free operation probability for a given time and guaranteed uptime, with a given guarantee level, for a system model with arbitrary redundancy modes, loaded or unloaded, in various subsystems. When studying the problem, we relied on the elements test results. Problems like that are often found in engineering practice when designing and experimentally developing modern complex engineering systems and their various components. The paper gives the construction of lower confidence limits for the indicated main indicators of the system reliability based on the available statistical information on the test results of its elements, and also presents approximate asymptotic (for the case of high reliability) expressions obtained for the lower confidence limit of the system reliability function
 Gnedenko B.V., Belyaev Yu.K., Solovev A.D. Matematicheskie metody v teorii nadezhnosti [Mathematical methods in reliability theory]. Moscow, LIBROKOM Publ., 2013, 584 p.
 Gnedenko B.V., ed. Voprosy matematicheskoy teorii nadezhnosti [Problems of mathematical reliability theory]. Moscow, Radio i Svyaz Publ., 1983, 376 p.
 Gnedenko B.V., Pavlov I.V., Ushakov I.A. Statistical reliability engineering. N.Y., John Wiley & Sons, 1999, 517 p.
 Belyaev Yu.K. Doklady AN SSSR (Proceedings of the USSR Academy of Sciences), 1967, vol. 196, no. 4, pp. 755–758.
 Belyaev Yu.K., Dugina T.N., Chepurin E.V. Izv. AN SSSR, Tekhnicheskaya kibernetika (Izv. USSR Academy of Sciences, Technical Cybernetics), 1967, no. 2, pp. 52–69.
 Pavlov I.V. Avtomatika i telemehanika — Automation and Remote Control, 2017, no. 3, pp. 149–158.
 Pavlov I.V., Razgulyaev S.V. Inzhenernyy zhurnal: nauka i innovatsii —Engineering Journal: Science and Innovation, 2015, iss. 2. DOI: 10.18698/2308-6033-2015-2-1365
 Pavlov I.V, Tedeluri M.M. Inzhenernyy zhurnal: nauka i innovatsii —Engineering Journal: Science and Innovation, 2018, iss. 1. DOI: 10.18698/2308-6033-2018-1-1719
 Pavlov I.V., Razgulyaev S.V. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki — Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2015, no. 4 (61), pp. 15–22.
 Pavlov I.V., Razgulyaev S.V. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki — Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2018, no. 5, pp. 37–44.
 Sadykhov G.S., Savchenko V.P., Sidnyaev N.I. Modeli i metody otsenki ostatochnogo resursa izdeliy radioelektroniki [Models and methods for assessing the residual life of the products of radio electronics]. Moscow, BMSTU Publ., 2015, p. 382.
 Asadi M., Bayramoglu I. The mean residual life function of a k-out-of-n structure at the system level (2006) IEEE Transactions on Reliability, vol. 55 (2), pp. 314–318.
 Lixuan Lu, Gregory Lewis. Configuration determination for k-out-of-n partially redundant systems. Reliability Engineering & System Safety, vol. 93, iss. 11, 2008, November, pp. 1594–1604.
 Wei-Chang Yeh. A simple algorithm for evaluating the k-out-of-n network reliability. Reliability Engineering & System Safety, vol. 83, iss. 1, January, 2004, pp. 93–101.
 Emmanuel J, Marquez R, Levitin G. Algorithm for estimating reliability confidence bounds of multi-state systems. Reliability Engineering & System Safety, 2008; iss. 93 (8), pp. 1231–1243.
 Hryniewicz O. Confidence bounds for the reliability of a system from subsystem data. RT&A? 2010, iss. 1, pp. 145–160.
 Goryainov V.B., Pavlov I.V., et al. Matematicheskaya statistika [Mathematical statistics], vol. 17. Krischenko A.P., Zarubin V.S., ed. Moscow, BMSTU Publ., 2008, 424 p.
 Zangwill W.I. Nonlinear programming: a unified approach. Prentice-Hall, 1969, 356 p. [In Russ.: Willard I. Zangwill. Nelineynoe programmirovanie. Ediny podhod. Mosoc, Sovetskoe Radio, 1973, 312 p.].